Related papers: Decomposable dynamics on matrix algebras

The type and several invariant subspaces related to the upper annihilating series of finite-dimensional nilpotent evolution algebras are introduced. These invariants can be easily computed from any natural basis. Some families of nilpotent…

We introduce a class of partial differential equations on metric graphs associated with mixed evolution: on some edges we consider diffusion processes, on other ones transport phenomena. This yields a system of equations with possibly…

We investigate completely positive maps for an open system interacting with its environment. The families of the initial states for which the reduced dynamics can be described by a completely positive map are identified within the framework…

In open quantum systems, it is known that if the system and environment are in a product state, the evolution of the system is given by a linear completely positive (CP) Hermitian map. CP maps are a subset of general linear Hermitian maps,…

The Gauss decompositions of the quantum groups, related to classical Lie groups and supergroups are considered by the elementary algebraic and $R$-matrix methods. The commutation relations between new basis generators (which are introduced…

We use symmetric measurement operators to construct quantum channels that provide a further generalization of generalized Pauli channels. The resulting maps are bistochastic but in general no longer mixed unitary. We analyze their important…

We generalize the result of Gorini, Kossakowski, and Sudarshan [J. Math. Phys. 17:821, 1976] that every generator of a quantum-dynamical semigroup decomposes uniquely into a closed and a dissipative part, assuming the trace of both…

We present the probability preserving description of the decaying particle within the framework of quantum mechanics of open systems taking into account the superselection rule prohibiting the superposition of the particle and vacuum. In…

Just like decent classical difference-difference systems define symplectic maps on suitable phase spaces, their counterparts with properly ordered noncommutative entries come as Heisenberg equations of motion for corresponding quantum…

Decompositions of the unitary group U(n) are useful tools in quantum information theory as they allow one to decompose unitary evolutions into local evolutions and evolutions causing entanglement. Several recursive decompositions have been…

We analyze a class of dynamics of open quantum systems which is governed by the dynamical map mutually commuting at different times. Such evolution may be effectively described via spectral analysis of the corresponding time dependent…

We address the question of the existence of quantum channels that are divisible in two quantum channels but not in three or, more generally, channels divisible in $n$ but not in $n+1$ parts. We show that for the qubit those channels…

Having a broad range of methods available for implementing unitary operations is crucial for quantum information tasks. We study a dissipative process commonly used to describe dissipatively coupled systems and show that the process can…

Master equations in the Lindblad form describe evolution of open quantum systems that is completely positive and simultaneously has a semigroup property. We analyze a possibility to derive this type of master equations from an intrinsically…

We introduce a generalization of the set of completely positive matrices that we call "pairwise completely positive" (PCP) matrices. These are pairs of matrices that share a joint decomposition so that one of them is necessarily positive…

We construct a new class of positive indecomposable maps in the algebra of `d x d' complex matrices. These maps are characterized by the `weakest' positivity property and for this reason they are called atomic. This class provides a new…

We consider a two-dimensional quantum control system evolving under an entropy-increasing irreversible dynamics in the semigroup form. Considering a phenomenological approach to the dynamics, we show that the accessibility property of the…

We study a notion of indecomposability in differential algebraic groups which is inspired by both model theory and differential algebra. After establishing some basic definitions and results, we prove an indecomposability theorem for…

We discuss dynamical response theory of driven-dissipative quantum systems described by Markovian Master Equations generating semi-groups of maps. In this setting thermal equilibrium states are replaced by non-equilibrium steady states and…

The construction of exactly-solvable models has recently been advanced by considering integrable $T\bar{T}$ deformations and related Hamiltonian deformations in quantum mechanics. We introduce a broader class of non-Hermitian Hamiltonian…